Adviser: W. Li
In this thesis we study the zeta functions arising from PGSp(4) over a nonarchimedean
local field. In this case, the complexes have dimension two, like PGL(3). However, the
vertices are distinguished as special and nonspecial vertices, unlike the case of PGL(3).
We define the (edge) zeta function as the counting function of the number of tailless closed
geodesics of all type-one or type-two edges, which has a closed form expression in terms
of parahoric Hecke operators. The main result shows that the zeta function satisfies a zeta
identity involving the Euler characteristic of the complex, the characteristic polynomial of
the recurrence relations of the Hecke algebra, the Iwahori-Hecke operator and the number
of special and nonspecial vertices. Moreover, we study the operators on nonspecial vertices.